Updated fluid equations

docs/source/FluidEquations.rst

@@ -3,12 +3,21 @@ Fluid Equations
 
 Below are the governing equations for the fluid:
 
-.. math:: \frac{\partial (\epsilon_g \rho_g)}{\partial t} + \nabla \cdot (\epsilon_g \rho_g U_g)  = 0
+Conservation of fluid mass:
+
+.. math:: \frac{\partial (\varepsilon_g \rho_g)}{\partial t} + \nabla \cdot (\varepsilon_g \rho_g U_g)  = 0
   :label: eqn::mass_cons
 
-.. math:: \frac{ \partial (\epsilon_g \rho_g U)}{\partial t} + \nabla \cdot (\epsilon_g \rho_g U_g U_g) + \epsilon_g \nabla p_g = \nabla \cdot \tau + {\bf g}
+Conservation of fluid momentum:
+
+.. math:: \frac{ \partial (\varepsilon_g \rho_g U)}{\partial t} + \nabla \cdot (\varepsilon_g \rho_g U_g U_g) + \varepsilon_g \nabla p_g = \nabla \cdot \tau + {\bf g} 
+           + \sum_{part} \beta (V_{part} - U_g)
   :label: eqn::mom_cons
 
-.. math:: \frac{\partial \epsilon_g}{\partial t} + \nabla \cdot (\epsilon_g  U_g)  = 0
-  :label: eqn::mass_eps
+Conservation of fluid volume:
+
+where $\sum_{part} \beta (V_{part} - U_g)$ is the drag term in which $V_{part}$ represents the particle velocity.
+
+.. math:: \frac{\partial \varepsilon_g}{\partial t} + \nabla \cdot (\varepsilon_g  U_g)  = 0
+  :label: eqn::mass_vareps